Re: On 1/4*Pi*epsilon in Coulomb's law

[James McLean <mclean@GENESEO.EDU>]

Ludwik Kowalski wrote:
> What is epsilon_zero? Why is it called permittivity?
> What kind of experiments had to be performed to find
> out that epsilon_zero happens to be equal to 8.85*10^-12
> SI units? Most students taking an introductory physics
> course, either in a high school or a college, never learn
> how to answer such questions. As far as they are
> concerned physics is dogmatic; it asks them to accepts
> things without understanding.
Curiously, I see the exact opposite as being 'dogmatic'.  Why should I
be forced to choose my unit based on what makes a formula simple?  What
could be more natural than choosing units without worrying about their
relationships?  To give an example, if I were to invent units of length
and volume, my first impulse would be to choose things readily
available, for instance a "fingerlength" for length and a "handfull" for
volume.  Only after working with the math for a while might someone say,
"Hey, if our unit of volume were fingerlength^3, we'd get rid of a
conversion factor and life would be easier."

So, from my point of view, the CGSE version of Coulomb's law is easier,
but not more "natural" nor less "dogmatic," than the SI version.

> The most important, in my opinion, was the elimination of
> two cgs systems, CGSE and CGSM. Why did physicist use
> two systems when one would be sufficient? Because they
> wanted to preserve practical units (volts, ampere, ohm, etc.)
> used by technologists. Units which were either too small or
> too large were not desirable from the point of view of
> "computational efficiency". ...
I don't believe that "computational efficiency" is the appropriate
term.  Computational ease is determined in the mantissa (thinking in
terms of scientific notation).  1.3245 x 4.55342 is much harder than 1E3
x 4E5.  But practical units were chosen for their exponents, that is,
their order of magnitude sizes.

This helps with _conceptual_ efficiency, not computational.  Tell
someone to drive 10 km or 6 miles, and they will immediately have a
rough idea of what you mean.  Tell them to drive 10,000 m of 30000 feet,
and their eyes will glaze over (or, at best, they will do the conversion
into km or miles).  So it seems to me that preserving the practical
units (or at least keeping new units in the same order of magnitude)
should be a very high priority for introductory courses.

--
Dr. James McLean                     phone: (716) 245-5897
Dept. of Physics and Astronomy       FAX:   (716) 245-5288
SUNY Geneseo                         email: mclean@geneseo.edu
1 College Circle
Geneseo, NY  14454-1401